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Voronoi Cones by Tom Walsh

Voronoi Cones by Tom Walsh
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2017-05-14 20:23
FunctionCoordinate GeometrySolid GeometryGeometric ConstructionLocus
In collections Developing fun games and puzzles with 3D printing for STEAM
This GeoGebra example demonstrates the spatial arrangement and geometric relationships of multiple cones partitioned via Voronoi diagram principles. Core mathematical concepts include Voronoi diagrams, conical surfaces, tangent lines, right triangles, and algebraic region division. Construction uses the Cone and Voronoi commands with point sets A1–B1–C1 and similar, incorporating piecewise functions, tangent lines, and right triangle geometry. Suitable for high school spatial geometry, university analytic geometry, and mathematical modeling interest exploration.

GeoGebra Commands & Parameters

  1. Cone((x(C2), y(C2), -5), C2, 5) → E2_1, F2_1, G2
  2. Cone((x(C2), y(C2), -5), C2, 5) → F2_2, G2_1, H2
  3. Cone((x(C3), y(C3), -5), C3, 5) → E3_1, F3_1, G3
  4. Cone((x(C3), y(C3), -5), C3, 5) → F3_2, G3_1, H3
  5. Voronoi(list1) → graph1
  6. Cone((x(C1), y(C1), (-c)), C1, c) → D1, E1, F1
  7. Cone((x(C2), y(C2), (-c)), C2, c) → D2, E2, F2
  8. Cone((x(C3), y(C3), (-c)), C3, c) → D3, E3, F3
  9. Cone((x(C4), y(C4), (-c)), C4, c) → D4, E4, F4
  10. Cone((x(C5), y(C5), (-c)), C5, c) → D5, E5, F5
  11. Cone((x(C6), y(C6), (-c)), C6, c) → D6, E6, F6
  12. Cone((x(C7), y(C7), (-c)), C7, c) → D7, E7, F7
  13. Cone((x(C8), y(C8), (-c)), C8, c) → D8, E8, F8
  14. Cone((x(C9), y(C9), (-c)), C9, c) → D9, E9, F9
  15. Cone((x(C10), y(C10), (-c)), C10, c) → D10, E10, F10
  16. Cone((x(C11), y(C11), (-c)), C11, c) → D11, E11, F11
  17. Cone((x(C12), y(C12), (-c)), C12, c) → D12, E12, F12
  18. Cone((x(C13), y(C13), (-c)), C13, c) → D13, E13, F13
  19. Cone((x(C14), y(C14), (-c)), C14, c) → D14, E14, F14
  20. Cone((x(C15), y(C15), (-c)), C15, c) → D15, E15, F15
  21. Cone((x(C16), y(C16), (-c)), C16, c) → D16, E16, F16
  22. Cone((x(C17), y(C17), (-c)), C17, c) → D17, E17, F17
  23. Cone((x(C18), y(C18), (-c)), C18, c) → D18, E18, F18

AI Drawing Prompt Reference

Draw a set of cones defined by multiple points, with their bases on the xOy plane and vertices on the z-axis at the same height. Then generate a Voronoi diagram using the vertices of these cones to show the boundaries between them.
The prompt above was compiled from the original drawing commands and is for reference only.